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In this paper we consider a distributed optimization scenario in which a set of processors aims at cooperatively solving a class of min-max optimization problems. This set-up is motivated by peak-demand minimization problems in smart grids.…

Optimization and Control · Mathematics 2016-11-29 Ivano Notarnicola , Mauro Franceschelli , Giuseppe Notarstefano

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

Optimization and Control · Mathematics 2025-06-03 Hongjin He , Kai Wang , Jintao Yu

Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…

Computational Physics · Physics 2026-05-26 Giuseppe De Laurentis , Jack Franklin

In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions…

Optimization and Control · Mathematics 2025-10-15 Cody Melcher , Afrooz Jalilzadeh , Erfan Yazdandoost Hamedani

In this paper, we introduce a practical GPU-enhanced matrix-free first-order method for solving large-scale conic programming problems, which we refer to as PDCS, standing for the Primal-Dual Conic Programming Solver. Problems that it…

Optimization and Control · Mathematics 2026-04-03 Zhenwei Lin , Zikai Xiong , Dongdong Ge , Yinyu Ye

We present a single-node, multi-GPU programmable graph processing library that allows programmers to easily extend single-GPU graph algorithms to achieve scalable performance on large graphs with billions of edges. Directly using the…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-02 Yuechao Pan , Yangzihao Wang , Yuduo Wu , Carl Yang , John D. Owens

This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…

Optimization and Control · Mathematics 2022-04-12 Hao Luo

We provide a preliminary study on utilizing GPU (Graphics Processing Unit) to accelerate computation for three simulation optimization tasks with either first-order or second-order algorithms. Compared to the implementation using only CPU…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-04-19 Jinghai He , Haoyu Liu , Yuhang Wu , Zeyu Zheng , Tingyu Zhu

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…

Optimization and Control · Mathematics 2025-08-26 Xiyan Hu , Titus Parker , Connor Phillips , Yifa Yu

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

Optimization and Control · Mathematics 2022-06-06 Xin He , Rong Hu , Ya-Ping Fang

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Optimization and Control · Mathematics 2016-05-11 Alexey Chernov , Pavel Dvurechensky , Alexander Gasnikov

The strict complementary slackness condition (SCSC) is an important concept in the duality theory of linear programming (LP). The current study aims at extending this concept to the framework of linear fractional programming (LFP). First,…

Optimization and Control · Mathematics 2016-03-03 Mahmood Mehdiloozad , Kaoru Tone , Mohammad Bagher Ahmadi

In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-27 Ivano Notarnicola , Mauro Franceschelli , Giuseppe Notarstefano

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

Optimization and Control · Mathematics 2022-02-10 Yujia Jin , Aaron Sidford , Kevin Tian

Parallel algorithms on CPU and GPU are implemented for the Unified Gas-Kinetic Scheme and their performances are investigated and compared by a two dimensional channel flow case. The parallel CPU algorithm has a one dimensional block…

Computational Physics · Physics 2018-11-02 Jizhou Liu , Fang Q. Hu , Xiaodong Li

Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often…

Computational Physics · Physics 2012-09-13 Tal Levy , Guy Cohen , Eran Rabani

We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of…

Machine Learning · Computer Science 2017-11-08 Celestine Dünner , Thomas Parnell , Martin Jaggi

The strategy of using CUDA-compatible GPUs as a parallel computation solution to improve the performance of programs has been more and more widely approved during the last two years since the CUDA platform was released. Its benefit extends…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-01-12 Chang Xu , Steven R. Kirk , Samantha Jenkins

Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…

Optimization and Control · Mathematics 2022-05-23 Xin He , Rong Hu , Ya-Ping Fang